French soldiers from the international coalition against the Islamic State group stand in front of a gun-howitzer near Al-Qaim in Iraq on February 9, 2019

Civilians fleeing fighting between Syrian Democratic Forces (SDF) and Islamic State group jihadists in eastern Syria wait to be screened by US-backed forces on February 3, 2019

Civilians fleeing fighting between Syrian Democratic Forces (SDF) and Islamic State group jihadists in eastern Syria wait to be screened by US-backed forces on February 3, 2019 (AFP Photo/Delil SOULEI[...]

Sousa (Syria) (AFP) - Syrian fighters backed by artillery fire from a US-led coalition battled a fierce jihadist fightback Monday as they pushed to retake a last morsel of territory from the Islamic State group.

Mushrooming black clouds rose over the embattled jihadist holdout in eastern Syria, as missiles and a warplane streaked through the sky.

More than four years after the extremists declared a "caliphate" across large parts of Syria and neighbouring Iraq, several offensives have whittled that proto-state down to a tiny holdout.

The Kurdish-led Syrian Democratic Forces (SDF) on Saturday announced the final push to expel hundreds of diehard jihadists from that patch on the Iraq border.

"IS launched a counterattack on our forces and we are now responding with rockets, air strikes and direct clashes," SDF spokesman Mustafa Bali told AFP Monday.

He said there were "dozens of SDF hostages held by IS" inside their last foothold, but denied reports of executions.

The Syrian Observatory for Human Rights, a Britain-based monitor, said the alliance of Kurdish and Arab fighters had pressed on Monday morning in the face of tough obstacles.

"The SDF are advancing slowly in what remains of the IS pocket" on the edges of the village of Baghouz, Observatory chief Rami Abdel Rahman said.

But landmines, IS snipers, and tunnels the extremists have dug out for their defence are hindering the advance, he said.

Backed by coalition air strikes, the SDF alliance has been battling to oust the jihadists from the eastern province of Deir Ezzor since September.

- Screening for jihadists -

Since December, tens of thousands of people, most women and children related to IS fighters, have fled to SDF territory.

US-backed forces have screened the new arrivals, weeding out potential jihadists for questioning.

On Monday, dozens of coalition and SDF fighters were stationed at a screening point for new arrivals from IS areas.

Coalition forces stood over about 20 men who were crouching on the ground.

Some 600 people were able to reach SDF territory on Sunday after fleeing the fighting, the Observatory said.

Among them, were 20 suspected IS members, including two French women, seven Turks, and three Ukrainians, said the monitor, which relies on sources inside Syria.

The SDF -- which has said it expects the final offensive to be over in days -- announced Sunday that it had taken some 40 positions from the jihadists following direct combat involving light weapons.

The alliance had earlier said that up to 600 jihadists as well as hundreds of civilians could remain inside a patch four square kilometres (one mile square).

Spokesman Bali said IS leader Abu Bakr al-Baghdadi, the man who pronounced the cross-border "caliphate" in 2014, was not among them, and likely not in Syria.

At the height of their rule, the jihadists imposed their brutal interpretation of Islamic law on a territory roughly the size of Britain.

But military offensives in both countries, including by the SDF, have since retaken the vast bulk of their territory.

The jihadists however retain a presence in Syria's vast Badia desert, and have claimed a series of deadly attacks in SDF-held areas.

- Planned US withdrawal -

US President Donald Trump in December shocked Washington's allies by announcing a full withdrawal of US troops from Syria as IS had been "beaten".

But the US military warned in a report published this month that IS "could likely resurge in Syria within six to twelve months and regain limited territory" if sustained pressure is not maintained.

In January an IS suicide bomber attacked a US patrol in the northeastern city of Manbij, killing four Americans, five SDF fighters and ten civilians.

The losses were the worst combat losses for the US in war-torn Syria since it launched the coalition to fight IS in 2014.

Trump's decision to withdraw US troops has left Syria's Kurds scrambling for safeguards.

A US departure makes them more vulnerable to a long threatened attack by neighbouring Turkey, who considers Kurdish fighters to be "terrorists", and dashes their dreams of autonomy.

The Kurds have largely stayed out of Syria's nearly eight-year civil war, instead building their own semi-autonomous institutions in the northeast of the country.

But the expected US pullout has seen them grappling to mend ties with the Damascus regime, which is against Kurdish self-rule.

Syria's war has killed 360,00 people and displaced millions since it started in 2011 with the brutal repression of anti-government protests.

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US secretary of state Mike Pompeo has said the state department will block an American-born woman who left Alabama to join Islamic State in 2014 from returning to the US. Hoda Muthana, 24, told the Guardian this week that she regretted leaving the US to join the terrorist group and wants to return from Syria with her 18-month-old son. Pompeo said on Wednesday that the US will refuse to take Muthana back, saying she is "not a US citizen".

WASHINGTON (AP) - An Alabama woman who joined the Islamic State group in Syria won't be allowed to return to the United States with her toddler son because she is not an American citizen, the U.S. said Wednesday. Her lawyer is challenging that claim.

President Donald Trump said Wednesday he is barring a US-born former Islamic State propagandist from returning home, making the highly unusual case that she is not a US citizen. Trump's refusal to admit 24-year-old Hoda Muthana comes just as he is pressing Europeans to repatriate their own Islamic State fighters and will likely face legal challenges, with US citizenship extremely difficult to lose. Trump said on Twitter he has "instructed" Secretary of State Mike Pompeo "not to allow Hoda Muthana back into the country" -- a break with usual US protocol not to comment on individuals' immigration issues.

The United States said Wednesday it would refuse to take back a US-born Islamic State propagandist who wants to return from Syria, saying that she is no longer a citizen. The refusal to admit 24-year-old Hoda Muthana could set precedent and face legal challenges as it is generally extremely difficult to lose US citizenship. "Ms. Hoda Muthana is not a US citizen and will not be admitted into the United States," Secretary of State Mike Pompeo said in a terse statement.